[SOLVED] Binomial distribution problem

*According to Chemical Engineering Progress, approximately 30% of all pipework failures in chemical plants are caused by operator error.*

*Suppose, for a particular plant, that out of a random sample of 20 pipework failures, exactly 5 are operational errors. ***Do you feel that the 30% figure stated above applies to this plant? Comment.**

I did the math and

$\displaystyle p(X=5)= 0.1789$

The book says that this answer means that the 30% figure is acceptable, but I don't understand why. I would have thought that the 30% figure would be acceptable if $\displaystyle p(X=5)$ was close to 1. Can someone help me understand this? Thanks